To complete the other answers, you should also take into account accessibility issue, especially if the color you choose for the form input somehow risks to blend in with other colors you might use, such as:

color from the input fields

characters colors (if the value is incorrect and you put the character in red, for instance)

colors of icons or warnings you might display when the data is incorrect...

and so on

A border (meaning 'a graphical way of delimiting your input form) might also be a good way to isolate that form, without having relying solely on color.

In short, you might consider always using a combination of both: color and graphical ways to emphasize a GUI element.

It really depends on the layout of the rest of the site. In my opinion it's good to have the form offset somehow, even if just with top/bottom borders - often you can make the whole thing a small box within the page. For something like a registration system, though, you might as well make the entire page the form - the less distractory extra-content the better.